[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5831/HMJ.2013.35.1.73

CERTAIN IDENTITIES OF ZETA FUNCTIONS ON A QUATERNION ALGEBRA

Kim, Insuk (Department of Mathematics Education, Wonkwang University)
Jun, Sungtae (Division of Mathematics and Computer Science, Konkuk University)

Publication Information

Honam Mathematical Journal / v.35, no.1, 2013 , pp. 73-82 More about this Journal

Abstract

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

Keywords

zeta function; order; quaternion algebra; hecke ring;

Citations & Related Records

Reference

1	M. Eichler, The basis problem for modular forms and the traces of Hecke operators. Springer-Verlag, Lecture Notes in Math., Vol.320, pp. 75-151, 1972.
2	R. Godement, Les fonctions ${\zeta}$ des algebras simples I, II, Seminaire Bourbaki, 1958/1959.
3	H. Hijikata, A. Pizer, T. Shemanske, The basis problem for modular forms on ${\Gamma}_0(N)$ Memoirs AMS, Vol.32 No.418, November, 1989.
4	S. Jun, The equalities between Brandt matrices on primitive orders, preprint.
5	S. Jun, On the representatives of modular forms on ${\Gamma}_0(N)$ , J. Algebra, Vol.64, pp. 340-390, 1980. DOI
6	A. Pizer, An algorithm for computing modular forms by theta series, J. KMS, Vol.34 No.4, pp. 808-816, 1997.
7	H. Shimizu, On the traces of Hecke operators, J. Fac. Sci. Univ. Tokyo, Vol.10, pp. 1-19, 1963.
8	H. Shimizu, On zeta functions of quaternion algebra, Ann. of Math., Vol.81, pp. 166-193, 1965. DOI
9	G. Shimura, "Introduction to the arithmetic theory of automorphic functions", Princeton Univ Press, Princeton, N.J., 1971.
10	T. Tamagawa, On ${\zeta}$ functions of a division algebra, Ann. of Math. Vol.77, pp. 387-405, 1963. DOI